Characterization for stability in planar conductivities
Faraco, Daniel (Universidad Autónoma de Madrid. Departamento de Matemáticas)
Prats, Martí (Universidad Autónoma de Madrid. Departamento de Matemáticas)

Date:	2018
Abstract:	We find a complete characterization for sets of uniformly strongly elliptic and isotropic conductivities with stable recovery in the L2 norm when the data of the Calderón Inverse Conductivity Problem is obtained in the boundary of a disk and the conductivities are constant in a neighborhood of its boundary. To obtain this result, we present minimal a priori assumptions which turn out to be sufficient for sets of conductivities to have stable recovery in a bounded and rough domain. The condition is presented in terms of the integral moduli of continuity of the coefficients involved and their ellipticity bound as conjectured by Alessandrini in his 2007 paper, giving explicit quantitative control for every pair of conductivities.
Grants:	European Commission 307179 Ministerio de Economía y Competitividad MTM2011-28198 Ministerio de Economía y Competitividad SEV-2015-0554 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-75
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Calderón Inverse Problem ; Complex Geometric Optics Solutions ; Integral modulus of continuity ; Quasiconformal mappings ; Stability
Published in:	Journal of differential equations, Vol. 264, Issue 9 (May 2018) , p. 5659-5712, ISSN 1090-2732

DOI: 10.1016/j.jde.2018.01.013

47 p, 945.5 KB

The record appears in these collections:
Articles > Research articles
Articles > Published articles